In their original paper, Kolmogorov, Petrovsky, and Piskunov demonstrated stability of the minimal speed traveling wave with an ingenious argument based on, roughly, the decreasing steepness of the profile.  This proof is extremely flexible, yet entirely not quantitative being based on compactness.  On the other hand, more modern PDE proofs of the stability of traveling waves solutions to reaction-diffusion equations are highly tailored to the particular equation, fairly complicated, and often not sharp in terms of the rate of convergence.  In this talk, I will introduce a natural quantity, the shape defect function, that allows a simple approach to quantifying convergence to the traveling wave for a large class of reaction-diffusion equations, including both pushed, pulled, and pushmi-pullyu equations.  This is a joint work with Jing An and Lenya Ryzhik.